Possibly I‘m not smart enough to understand, but from what I see is that the implementers intend to leverage existing security architecture of Android/Google and iOS/Apple, respectively- arguably to drive adoption. The document doesn’t state anywhere that Apple / Google account is a requirement to use German eIDAS. From what I can tell, one may (continue to) use its government issued ID card with electronic signature for authentication.
Please prove me wrong, I genuinely want to understand the implication of the linked document.
The account is not directly required, but you have a very hard time using an Android smartphone without a Google account. It's a bit easier with Apple, however both have in common that the apps required for eIDAS are available in their app stores – and they are not usable without an account (for common users).
It's an account requirement in a roundabout way.